Multiplier-integrator circuit



Feb. 3, 1959 B, D, sMl'n-l,v JR 2,872,109

MULTIPLIER-INTEGRATOR CIRCUIT Filed Oct. 29, 1955 United States Patent()2,872,109 MULTIPLIER-INTEGRATOR CIRCUIT Blanchard D. Smith, Jr.,Alexandria,

United States of America as tary of the Air Force Va., assgnor to therepresented by the Secre- It is the object of this invention to providea circuit capable of producing an output voltage that is proportional tothe integral over a period of time of the product of two voltages thatare functions of time.

The circuit consists essentially of a condenser and means for initiallycharging the condenser to a predetermined starting voltage. Thecondenser is arranged to discharge through a device the current iiowthrough which is substantially independent of condenser voltage butproportional to one of the input signals. Such a device may be a highgain amplifier tube, such as a pentode, employing current negativefeedback. Conduction through the above device, however, is preventedexcept during periodically occurring intervals the durations of whichare pro portional to the second input voltage. At the end of the periodof integration the condenser potential is less than its initial valueand this difference is proportional to the integral of the product ofthe two input signals.

A more detailed description of the invention will be given in connectionwith the accompanying drawings, in which Fig. l is a schematic circuitdiagram of the multiplierintegrator; and

Fig. 2 illustrates the performance of the a single integration.

Referring to Fig. l, the multiplier-integrator circuit is provided withinput terminals 1 and 2 to which input signals E1=f1() and E4=f2(t) areapplied. The value of the integral of the product of these two functionsover a period of time appears at terminals 3 and equals E2E Ep beingsubstantially equal to Ec as will be seen later. Tube 4 is a high gainpeutode having its screen grid G2 at a fixed potential E3. Theanode-cathode circuit of the tube contains condenser C, which suppliesthe anode voltage for the tube during integration, resistor R and inputsignal source E1. Resistor R and source E1 are also ineluded in thegrid-cathode circuit of the tube so that the common resistor provides acurrent negative feedback to the input circuit of the tube. A source E2and switch S1 are provided for initially charging condenser C. Grid G3,the suppressor grid, has applied to it a series of rectangular pulseswhich are width modulated so that the ratio w/ T is proportional to E4and has a maximum value not exceeding unity. This modulation isaccomplished by the pulse Width modulator 5 which may be a circuit ofthe phantastron type, such as described on pages 195- 204, vol. 19,Radiation Laboratory Series, McGraw-Hill, or any other known circuitcapable of performing the required pulse modulation. Certain of thesecircuits require trigger pulses which for this reason are illustrated asbeing applied to terminal 6. The circuit is so adjusted that conductionbetween anode and cathode in tube 4 can take place only during theinterval w of the square wave applied to G3. In the example shown thevoltage of the square wave is zero during time w and negative at allother times.

To perform an integration, condenser C is irst charged to a voltage E2by momentarily closing S1. The concircuit during ICC- denser chargesrapidly due to the low resistance of the grid-cathode space path of tube4. The functions represented by the voltages E1 and E4 are then appliedto terminals 1 and 2 for the interval of integration t. At the end ofthis interval the voltage Ez-Ep at terminals 3 represents the value ofthe integral K f ofElEzdt.

To analyze the operation of the circuit lirst consider the situation inwhich E4=0. For this condition w=0 and plate conduction in tube 4 cannot occur at any time during the interval of integration. Therefore Ccan not discharge and its voltage at the end of the interval remains atthe value E2. Further, the voltage of G1 is substantially zero since itcannot exceed that of the cathode because of R and grid-cathodeconduction. The voltage at terminals 3, which represents the value ofthe integral, is therefore zero. For the condition E1=0, the dischargeof C is likewise prevented and the value of the integral is zero. Thereason for this is that any attempt for C t0 discharge through theanode-cathode path of tube 4 and resistor R is opposed by the resultingnegative potential on G1 due to R, or, in other words, by the resultingnegative feedback. If the amplication of the tube is high the impedanceoffered to the discharge current is high and substantially no change incondenser voltage takes place during the integration interval. Thevoltage of G1 remains substantially zero in this condition also since,with E1=O, there is nothing to drive it in a positive direction and thehigh mutual conductance of the grid prevents any appreciable movement inthe negative direction due to anode current flow in R.

vThe usual condition is that in which both E, and E4 are greater thanzero. In this condition also, the presence of R and the high mutualconductance of G1 prevent this grid from departing by any appreciableamount from the cathode potential, so that its potential is alwayssubstantially zero. Considering the operation during the period w,condenser C discharges through the anode-cathode path of tube 4, sourceE1 and resistor R. Due to the negative feedback produced by R and thehigh mutual conductance of G1 the discharge current through R issubstantially independent of the condenser voltage Ec and isproportional to El. During the time interval w, therefore, the charge oncondenser C is decreased by an amount proportional to w and thedischarge current. Since w is proportional to E4 and the dischargecurrent, as stated above, is proportional to E1, the decrement incondenser voltage Ec during each pulse on G3 is proportional to theproduct EIEAX. During the time when the voltage on G3 is negative andthe anode current of tube 4 is cut otf, C cannot discharge and Ecremains constant. The voltage Ec therefore decreases in steps during theintegration interval, each decrement being proportional to EIE., at thetime, so that the total decrement at the end of the interval isproportional to the integral of BIE, over that period of time. Thisdecrement may be measured across terminals 3 since, as has been stated,G1 remains at substantially zero or ground potential. so thatEZ-EpzKfofElEldL The constant K is a function of RC and the degree ofpulse width modulation caused by E4. The frequency of the pulsesmodulated by E4 should be high enough to accurately follow the envelopeof E4.

The above process is illustrated in Fig. 2. The square wave of voltageapplied to G3 is shown along the horizontal axis. As is evident, thedecrement in Ec, AEC, during each interval w is proportional to theslope of the linear discharge curve and to the size of w. This decrementis therefore proportional to E1E4 since the slope is proportional to Eland w is proportional to E4.

l claim:

l. A circuit for reducing the charge in a condenser by an amountproportional to the integral of the product of two varying signalvoltages over a desired integration Patented Feb. 3, 1959` germesinterval, said circuit comprising means operative during said intervalfor periodically discharging said condenser through a device the currentthrough which is substantially independent of the condenser voltage andis proportional to one of said signal voltages, and means forcontrolling the durations of the periodic discharges in proportion tothe other of said signal voltages.

2. A circuit for producing a voltage proportional to the integral of theproduct ot twotvoltages over a desired integration interval, saidcircuit comprising a condenser, means for initially charging saidcondenser to a predetermined potential, means operative during saidinterval for periodically discharging said condenser through a devicethe current through which is substantially independent of the condenservoltage and is proportional to one of said signal voltages, means forcontrolling the durations of the periodic discharges in proportion tothe other of said signal voltages, and means for deriving the differencebetween said predetermined potential and the potential across saidcondenser at the end of said interval.

3. A circuit for reducing the charge on a condenser by an amountproportional to the integral of the product of two varying voltages overa desired integration interval, said circuit comprising a high gainamplifier tube having an anode, a cathode and a control grid; meansconnecting said condenser, a resistor and one of said two voltages inseries between the anode and cathode of said tube; means for alsoconnecting said resistor and said one voltage between the control gridand cathode of said tube; and means for blocking anode conduction insaid tube except during periodically occurring discharge periods withinsaid interval the lengths of which are proportional to the other of saidtwo voltages.

4. Apparatus as claimed in claim 3 in which said last named meanscomprises a second grid in said tube located between the anode and saidcontrol grid, means for applying a rectangular Vvoltage wave to saidsecond grid of such voltage relative to the cathode of said tube thatanode conduction is prevented except during the positivegoing portionsof said wave, and means for controlling the durations of saidpositive-going portions in proportion to the other of said two voltages.

5, A circuit for producing a voltage proportional to the integral of theproduct of two voltages over a desired integration interval, saidcircuit comprising a condenser; a high gain amplitier tube having ananode, a cathode and a control grid; means connecting said condenser aresistor and one of said two voltages in series between the anode andcathode of said tube; means for also connecting said resistor and saidone voltage between the control grid and cathode of said tube; means forblocking anode conduction in said tube except during periodicallyoccurring discharge periods within said interval the lengths ot whichare proportional to the other of said two voltages; means formomentarily applying a direct voitage between said anode and cathode forinitially charging said condenser; and means for deriving the differencebetween said direct voltage and the voltage of said anode at the end ofsaid integration interval.

References Cited in the file of this patent UNlTED STATES PATENTS2,491,779 Y Swantzel June ll, 1946 2,433,237 Rajchman Dec. 23, 19472,486,068 Shishini Oct. 25, 1949 2,643,819 Lee et al. June 30, i9532,675,469 Harker Apr. 13, 1954 OTHER REFERENCES Korn and Korn ElectronicAnalog Computers, Mc- Graw-Hill Book Co., New York, Toronto, Canada1952, Electronic Engineering, August 1948, pages 244-246.

